Finite Group DatabasebetaFinite Group Databasebeta| order | 21248 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C83 · Schur multiplier (H2) = C24 |
| direct product | C83×#17927 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C83 | C22×D4 |
| commutator | C2×C4 | C23×C4×C83 |
| Frattini, cosocle | C42 | C24×C83 |
| socle | C22×C83 | C2×C4×D4 |
| prime radical | #449×C83 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C83 ◁ #431×C83 ◁ G | |
620 conjugacy classes of subgroups.
| minimal degree | μ(G) = 115 |
| transitive degree | μt(G) = 10624 |
A minimal faithful permutation representation — 4 generators on 115 points:
(1,2,7,12)(3,13,4,9)(5,11,6,10)(8,15,16,14)(17,18,20,24,21,23,27,30)(19,22,25,29,26,28,31,32)(33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115);(1,3,7,4)(2,8,12,16)(5,14,6,15)(9,10,13,11);(1,4,7,3)(2,9,12,13)(5,14,6,15)(8,10,16,11)(17,19,20,25,21,26,27,31)(18,22,24,29,23,28,30,32);(1,5,7,6)(2,10,12,11)(3,14,4,15)(8,13,16,9)(18,23)(22,28)(24,30)(29,32)5312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21248, 10915);